I'd suggest contacting your local housing authority to see if they will partner with you to resolve the issue or remove her and revoke her voucher.  

I was unexpectedly approached by a family with a section 8 voucher for $1100, which is the market allowance for a 4br in Providence.

The one exception is that if a PHA issues 1 Bedroom rate vouchers to 1 person households, they may elect at some point to move those vouchers to studio rate vouchers (0 bedroom rate), which could serious impact the rate that new tenants could rent at, but again would not change the total amount of rent collected by you for tenants currently under a rental agreement.

They can withhold your check if they find a violation, and it can take a while for them to get their paperwork together to get your money coming again.So, if you don't absolutely have to accept Section 8, I wouldn't.The exception would be if you have a current tenant you like, who gets their Section 8 voucher after they've been in your building awhile, and they ask you to accept their Section 8, so they can stay - then it might be worth doing.And from my understanding, if you do this, you are not required to then accept Section 8 for all of your other tenants. 

Please refer to HUD's website to read more about the Fair Housing Act.As @Ned Carey said, there are some additional jurisdictional-specific protected classes that some States and Counties decided to enforce to supplement the national Fair Housing Act, one of which is protection on the basis of income source (aka vouchers). 

If you have the voucher number call up Section 8 and ask.

Finding out about them can be word of mouth, researching programs in the local area, or just advertising that you will consider voucher programs and see what comes your way.Good luck!

It seemed the current property management company didn’t like dealing with Section 8 tenants, so they chose only to accept 1 and 2 bedroom vouchers so as to have physically less people in the units to deal with.

Just ignore his calls going forward, in that case.I am currently a Section 8 voucher holder, and I can tell you that most recipients won't meet strict criteria. 

Anyway, the new tenant has a gov’t caseworker, I knew that when I signed his voucher and went over the lease.